White to Transparent does not work when saved

1. Open new gimp project. The background will be either the current foreground or background color. The point is it's ONE solid color.
2. Layer->Transparency->Add Alpha Channel
3. Edit->Clear The color is gone and it's a transparent layer. This is what I want to save.
4. File -> Save As (version 2.6)
5. Type in test.jpg
6. Open up test.jpg and you will see the transparent layer from step 3 has magically gone to white.